Module 6. Unsteady state heat transfer
Lesson 29
ASSIGNMENTS
Q. 1. The wall of a steam boiler furnace which is not with water walls is made of layer of formed fireclay of thickness δ1 = 125 mm and a layer of red brick 500 mm thick (δ2). The two layers fit each other tightly. The wall temperature inside the boiler furnace tW1 = 1100°C and the wall outside temperature tW3 =50°C. The thermal conductivity of formed fireclay λ1 = 0.28+0.00023t and that of the red brick, λ2 = 0.7 W/m-°C. Calculate the amount of the heat lost from 1 m2 of the furnace wall by conduction and the temperature at the layer interface.
ANSWERS
The loss of heat or the rate of heat flow through the wall q = 1032 W/m2. The temperature at the layer interface tW2 = 787°C.
Q. 2. A reinforced-concrete smoke stack with an inner diameter d2 = 800 mm and outer diameter d2 = 1300 mm must be lined with a refectory on the inside. Determine the refectory lining and the temperature of the outer surface of the smoke stack, tW3, under conditions that the loss of heat from length of 1m of the smoke stack must not exceed 2000W/m and the temperature of the inner surface of the reinforced-concrete smoke stack, tW2, should not exceed 200°C. The temperature of the inner surface of the lining refectory tW1 = 425°C; the thermal conductivity of the lining λ1 = 0.5 W/m-°C; the thermal conductivity of concrete λ2 = 1.1 W/m-°C.
ANSWERS
δ = 120 mm. The temperature of the tube outer surface tW3 = 59°C.
Q. 3. Determine the time τ required to heat a steel plate of thickness 2δ = 24 mm from the initial temperature t0 = 25°C to the final temperature the = 450°C by placing the plate into a furnace in which the temperature tf = 600°C is maintained. The thermal conductivity, heat capacity and the density of steel are respectively λ = 45.4 W/m-°C, c = 0.502 kJ/kg-°C and ρ = 7800 kg/m3; the local coefficient of heat transfer from the hot surroundings from the hot surroundings in the furnace to the surface of the steel plate α = 23.3 W/m2-°C.
ANSWER
τ = 45 min.